A photographer connects ancient cities and modern metropolises in his panoramic images.

“The horizon is such a basic way of comprehending the space around us, comprehending our basic relationship to the globe If the horizon seems to offer possibilities,it also establishes a boundary. “In terms of looking, the horizon is the farthest we can see, yet in terms of knowledge, it reflects “the limit of experience.”

(Mrs. Morninghouse, after a Sermon Entitled,
“What the Spirit Teaches Us through Grief”)

The shape of her soul is a square.
She knows this to be the case
because she sometimes feels its corners
pressing sharp against the bone
just under her shoulder blades
and across the wings of her hips.
At one time, when she was younger,
she had hoped that it might be a cube,
but the years have worked to dispel
this illusion of space. So that now
she understands: it is a simple plane:
a shape with surface, but no volume—
a window without a building, an eye
without a mind.
Of course, this square
does not appear on x-rays, and often,
weeks may pass when she forgets
that it exists. When she does think
to consider its purpose in her life,
she can say only that it aches with
a single mystery for whose answer
she has long ago given up the search—
since that question is a name which can
never quite be asked. This yearning,
she has concluded, is the only function
of the square, repeated again and again
in each of its four matching angles,
until, with time, she is persuaded anew
to accept that what it frames has no
interest in ever making her happy.

After 38 Years, Israeli Solves Math Code
JERUSALEM — A mathematical puzzle that baffled the top minds in the esoteric field of symbolic dynamics for nearly four decades has been cracked — by a 63-year-old immigrant who once had to work as a security guard.

Avraham Trahtman, a mathematician who also toiled as a laborer after moving to Israel from Russia, succeeded where dozens failed, solving the elusive ”Road Coloring Problem.”

The conjecture essentially assumed it’s possible to create a ”universal map” that can direct people to arrive at a certain destination, at the same time, regardless of starting point. Experts say the proposition could have real-life applications in mapping and computer science.

The ”Road Coloring Problem” was first posed in 1970 by Benjamin Weiss, an Israeli-American mathematician, and a colleague, Roy Adler, who worked at IBM at the time.

For eight years, Weiss tried to prove his theory. Over the next 30 years, some 100 other scientists attempted as well. All failed, until Trahtman came along and, in eight short pages, jotted the solution down in pencil last year.

”The solution is not that complicated. It’s hard, but it is not that complicated,” Trahtman said in heavily accented Hebrew. ”Some people think they need to be complicated. I think they need to be nice and simple.”

Weiss said it gave him great joy to see someone solve his problem.

Stuart Margolis, a mathematician who recruited Trahtman to teach at Bar Ilan University near Tel Aviv, called the solution one of the ”beautiful results.” But he said what makes the result especially remarkable is Trahtman’s age and background.

”Math is usually a younger person’s game, like music and the arts,” Margolis said. ”Usually you do your better work in your mid 20s and early 30s. He certainly came up with a good one at age 63.”

Adding to the excitement is Trahtman’s personal triumph in finally finding work as a mathematician after immigrating from Russia. ”The first time I met him he was wearing a night watchman’s uniform,” Margolis said.

Originally from Yekaterinburg, Russia, Trahtman was an accomplished mathematician when he came to Israel in 1992, at age 48. But like many immigrants in the wave that followed the breakup of the Soviet Union, he struggled to find work in the Jewish state and was forced into stints working maintenance and security before landing a teaching position at Bar Ilan in 1995.

The soft-spoken Trahtman declined to talk about his odyssey, calling that the ”old days.” He said he felt ”lucky” to be recognized for his solution, and played down the achievement as a ”matter for mathematicians,” saying it hasn’t changed him a bit.

The puzzle tackled by Trahtman wasn’t the longest-standing open problem to be solved recently. In 1994, British mathematician Andrew Wiles solved Fermat’s last theorem, which had been open for more than 300 years. Trahtman’s solution is available on the Internet and is to be published soon in the Israel Journal of Mathematics.

Joel Friedman, a math professor at the University of British Columbia, said probably everyone in the field of symbolic dynamics had tried to solve the problem at some point, including himself. He said people in the related disciplines of graph theory, discrete math and theoretical computer science also tried.

”The solution to this problem has definitely generated excitement in the mathematical community,” he said in an e-mail.

Margolis said the solution could have many applications.

”Say you’ve lost an e-mail and you want to get it back — it would be guaranteed,” he said. ”Let’s say you are lost in a town you have never been in before and you have to get to a friend’s house and there are no street signs — the directions will work no matter what.”

Most people remember James Clerk Maxwell for his equations relating electric and magnetic fields, which revolutionized 19th-century science. But the Scottish physicist and mathematician was also an amateur poet, and this small collection, hosted by the University of Toronto, offers a rare insight into his opinions and personality:

Gin a body meet a body
Flyin’ through the air,
Gin a body hit a body,
Will it fly? and where?

That’s a “Rigid Body,” “singing,” in Maxwell’s verse “In Memory of Edward Wilson, Who Repented of What Was in His Mind to Write After Section”—a pastiche of Maxwell’s countryman Robert Burns. (“Section” here probably refers to a meeting of the British Association devoted to mathematics and physics.) It’s said that Maxwell used to sing these lines while accompanying himself on a guitar.

Also here are the revealingly whimsical “Molecular Evolution”:

What combinations of ideas,
Nonsense alone can wisely form!
What sage has half the power that she has,
To take the towers of Truth by storm?

… and the regrettable “Lectures to Women on Physical Science” (“To mirror heaven those eyes were given / And not for methods of precision”), as well as three other poems. Together they give a telling glimpse into the reflective and playful inner life of a giant in the canon of physics.

Molecular Evolution

At quite uncertain times and places,
The atoms left their heavenly path,
And by fortuitous embraces,
Engendered all that being hath.
And though they seem to cling together,
And form “associations” here,
Yet, soon or late, they burst their tether,
And through the depths of space career.
So we who sat, oppressed with science,
As British asses, wise and grave,
Are now transformed to wild Red Lions,
As round our prey we ramp and rave.
Thus, by a swift metamorphosis,
Wisdom turns wit, and science joke,
Nonsense is incense to our noses,
For when Red Lions speak, they smoke.
Hail, Nonsense! dry nurse of Red Lions,
From thee the wise their wisdom learn,
From thee they cull those truths of science,
Which into thee again they turn.
What combinations of ideas,
Nonsense alone can wisely form!
What sage has half the power that she has,
To take the towers of Truth by storm?
Yield, then, ye rules of rigid reason!
Dissolve, thou too, too solid sense!
Melt into nonsense for a season,
Then in some nobler form condense.
Soon, all too soon, the chilly morning,
This flow of soul will crystallize,
Then those who Nonsense now are scorning,
May learn, too late, where wisdom lies.

Notes
11] “The `Red Lions’ are a club formed by Members of the British Association, to meet for relaxation after the graver labours of the day.” (Note by Campbell.)
17] “Leonum arida nutrix.” — Horace. (Note by Campbell.)